NAME
CHER2K - perform one of the hermitian rank 2k operations C
:= alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
beta*C,
SYNOPSIS
SUBROUTINE CHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
BETA, C, LDC )
CHARACTER*1 UPLO, TRANS
INTEGER N, K, LDA, LDB, LDC
REAL BETA
COMPLEX ALPHA
COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
CHER2K performs one of the hermitian rank 2k operations
or
C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
beta*C,
where alpha and beta are scalars with beta real, C is
an n by n hermitian matrix and A and B are n by k
matrices in the first case and k by n matrices in the
second case.
PARAMETERS
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or
lower triangular part of the array C is to be
referenced as follows:
UPLO = 'U' or 'u' Only the upper triangular part
of C is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part
of C is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be per-
formed as follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( B' )
+ conjg( alpha )*B*conjg( A' ) + beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*B
+ conjg( alpha )*conjg( B' )*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N
must be at least zero. Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the
number of columns of the matrices A and B, and
on entry with TRANS = 'C' or 'c', K specifies
the number of rows of the matrices A and B. K must
be at least zero. Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
ka is
A -
COMPLEX array of DIMENSION ( LDA, ka ), where
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading
n by k part of the array A must contain the matrix
A, otherwise the leading k by n part of the array
A must contain the matrix A. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as
declared in the calling (sub) program. When
TRANS = 'N' or 'n' then LDA must be at least max(
1, n ), otherwise LDA must be at least max( 1, k ).
Unchanged on exit.
kb is
B -
COMPLEX array of DIMENSION ( LDB, kb ), where
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading
n by k part of the array B must contain the matrix
B, otherwise the leading k by n part of the array
B must contain the matrix B. Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as
declared in the calling (sub) program. When
TRANS = 'N' or 'n' then LDB must be at least max(
1, n ), otherwise LDB must be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. Unchanged
on exit.
C - COMPLEX array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading
n by n upper triangular part of the array C must con-
tain the upper triangular part of the hermitian
matrix and the strictly lower triangular part of C
is not referenced. On exit, the upper triangular
part of the array C is overwritten by the upper tri-
angular part of the updated matrix. Before entry
with UPLO = 'L' or 'l', the leading n by n lower
triangular part of the array C must contain the lower
triangular part of the hermitian matrix and the
strictly upper triangular part of C is not refer-
enced. On exit, the lower triangular part of the
array C is overwritten by the lower triangular part
of the updated matrix. Note that the imaginary parts
of the diagonal elements need not be set, they are
assumed to be zero, and on exit they are set to
zero.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as
declared in the calling (sub) program. LDC
must be at least max( 1, n ). Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989. Jack Dongarra,
Argonne National Laboratory. Iain Duff, AERE
Harwell. Jeremy Du Croz, Numerical Algorithms Group
Ltd. Sven Hammarling, Numerical Algorithms Group
Ltd.